Al-Kitab Journal for Pure Science

Al-Kitab Journal for Pure Science Issue 1, Volume 2, October 2018 DOI: 10.32441/kjps.v2i1.129 ISSN: (2617-1260)

Web Site: http://www.isnra.com/ojs/index.php/KJPS E-mail: [email protected]

1

“An experimentally investigate the fin thermal performance to the

different fin spaces by natural convections”

Dr. Hazim Abd Mohammed Al-Jewaree

Petroleum Engineering Department, Alkitab College University

E-mail: mailto:[email protected]

Abstract:

In oil and gas industries there are a lot off heat transfer devices used for different

purposes. These devices are widely used in various industrial, transportation, or

domestic applications such as heat exchangers thermal power plants, means of

transport, heating and air conditioning systems, electronic equipments and space

vehicles. In all these applications, improvements in the efficiency of heat exchangers

can lead to substantial cost, space and materials savings. The research work

summarized in this articles presents an experimental investigation on the effect of fin

space (s) and aluminum materials on the fin performance using rectangular fins. The

steady-state natural convection heat transfer from vertical rectangular fins extending

perpendicularly from horizontal square base was investigated experimentally at new

range not found in the previous works, this range of temperatures from 50 to 150 Co

.

The effects of fin space parameter and base-to-ambient temperature difference on the

heat transfer performance of fin arrays were observed and the environmental condition

were determined. Five fin space settings,( 22, 27, 30, 35 and 38 mm) with a constant fin

height is 50mm for all types of configuration are presented in this work were employed

under free convection heat transfer conditions. This range of fin space not found on

previous study or research. The heat transfer area was kept the same. The performance

of the fin expressed in terms of fin efficiency, effectiveness and thermal resistance as a

function of the ambient temperature and fin space parameters has been study in this

work. The dimensionless parameter Biot no. on the locally variable environmental

condition is examined for different fin spaces to the fin heat transfer rate. Also, the

effect of environmental condition is study. Experimental results show that the effect fin

space on fin performance is more significant.. The maximum increase in convection

heat transfer coefficient value obtained is about 22 percent. The increase in heat transfer

coefficient value is also manifested by a corresponding decrease in the fin base

temperature. Also, it is concluded from the experimental results that the performance of

heat transfer rate increase with decreasing the fin space in respect of heat transfer

coefficient, thermal resistance ,overall efficiency and effectiveness.

Key Word: (Fin space, Rectangular Fin , Natural Convection, Heat Transfer Performance) .

https://doi.org/10.32441/kjps.v2i1.129

mailto:[email protected]



2

دراسة عملية لقياس الاداء الحراري للزعانف في حالة تغير المسافات بينهما بواسط أنتقال الحرارة الطبيعي.

: الخلاصة

صناعات النفط والغاز أدى الى أستخدام الكثير من أجهزة أنتقال الحرارة لأغراض متعددة . وكذلك تستخدم التطور الكبير في هذه الأجهزة على نطاق واسع في مختلف التطبيقات الصناعية ، ووسائط النقل ، أو ضمن الصناعات المحلية مثل المبادلات

وتكييف الهواء ، واجهزة الحاسوب والمعدات الإلكترونية والمركبات الحرارية ومحطات الطاقة الحرارية ، وأنظمة التدفئة الفضائي. وتلعب الزعانف دور كبير في الحفاظ على هذه الاجهزة الحرارية وعملها المستمر لذلك ازدادت البحوث في هذا

ى توفير كبير من التكاليف المجال . في جميع هذه التطبيقات ، يمكن أن تؤدي التحسينات في كفاءة المبادلات الحرارية إلوالفضاء والمواد. يقدم بحثنا هذا تلخيصه تجريبيا حول تتحسين نقل الحرارة بواسطة الزعانف والمصنعة من معدن الألومنيوم

بشكله المألوف المستطيل. اعدة مربعة أفقية تم أنتقال الحرارة المنتظم للحمل الحراري الطبيعي من زعانف مستطيلة عمودية تمتد بشكل عمودي من قمئوي, 005إلى 05فحصها عمليا في نطاق جديد غير موجود في الأعمال السابقة ، وهو المدى الكبير لدرجات الحرارة من

وكذلك الفراغ بين الزعانف حيث تم أختبار تأثير المسافة بين الزعانف المصطفة على القاعدة. حيث تم استخدام خمس مسافات مم وكذلك ثبات مقدار 05ملم( بارتفاع ثابت للزعانف 03و 00، 05، 22، 22نف المصطفة وهي )مختلفة بين الزعا

العرض والسمك لجميع أنواع الزعانف المستخدمة في عملنا هذا عند ظروف نقل الحرارة بالحمل الحر. كما تم دراسة تاثير ثير درجة حراة المحيط الجوي. كل ماذكر أعلاه تم أختباره عمليا النتائج في حالة الظروف العمل اليومي ) نهارا وليلا ( اي تا

على الاداء الحراري لعمل الزعانف. ويتم قياس الاداء الحراري بواسطة القياسات العملية الدقيقة لكل من كفاءة الزعنفة عدد الثابت للزعانف . أيضا تم حساب وفعاليتها ومقاومتها الحرارية كدالة في درجة الحرارة المحيطة وتحت المساحة السطحية وال

. Biotمعامل عدد بيوت وهو معامل بدون أبعاد أظهرت النتائج التجريبية أن هناك تأثير واضح في درجات الحرارة وكذلك المسافة بين الزعانف على أداء الزعانف الحراري

لزيادة القصوى في قيمة معامل انتقال الحرارة الحراري الحرارة. بلغت ا أنتقالوالتي اثبتت المسافة او الفراغ أكثر أهمية في ٪. تتجلى أيضا الزيادة في قيمة معامل نقل الحرارة بانخفاض مماثل في درجة حرارة القاعدة. أيضا ، تبين من النتائج 22حوالي

باشر على ، المقاومة الحرارية ، التجريبية أن أداء معدل نقل الحرارة يزداد مع تقليل المسافة بين الزعانف والذي يعتمد بشكل مالكفاءة والفعالية للزعانف بشكل عام.اما تاثير العمل نهارا او ليلا فوجد هناك فرق بسيط في الاداء اليلي لعمل الزعانف بسبب

الفرق ممكن أهماله لانه بسيط جدا. امخفاض حراة الليل عن النهار وهذا




3

I. Introduction:

In the free-convection cooling of electronic and thermoelectric devices, as well as in improving

the heat transfer in radiators for air conditioning and in other heat exchangers, finned surfaces are

extensively used. Compared to a bare plate, a finned surface increases the heat transfer area.

However, with the fins the flow rate reduced. Hence, if not properly designed it is possible that

no improvement achieved in terms of overall heat transfer. Therefore, only if the fins properly

designed, they are very attractive for these applications, since they offer an economical, trouble-

free solution to the problem. Extended surfaces, which are popularly known as fins, are

extensively used in air-cooled automobile engines and in air-cooled aircraft engines. Fins are also

used for the cooling of computer processors, and other electronic devices. Fins are used in the

cooling of oil carrying pipe line which runs several hundreds of miles. Heat pipes are also used

along with fins to enhance cooling rate. A great deal of research effort has been developed for

developing apparatus and performing experiments to define the conditions under which an

agentive technique will improve heat transfer. The more effective and feasible techniques have

graduated from laboratory to full-scale industrial equipment.

Starner and McManus [ 1 ] study experimentally very early in the heat transfer performance for

arrays of rectangular fins by natural convection. They used four sets of fins array at different

position (horizontal, 45 degree and vertical) based on the main heater at constant temperature 40 oC. They found the heat transfer coefficient for vertical position less than others by 10 to

30%.Leung and prober, [2] did another experimentally investigate the effect of fin height to the

fin space for optimum ratio at two rectangular fins array positions ( vertical and horizontal) . The

results for the range used from 20 to 40 oC , shows the optimum fin spacing value were 9 to 11

mm . It was also found that not affect orientation considering to the change of fin height and

base-to-ambient temperature difference.

Leung, Probert and Shilston [3] carried out experimental work for rectangular fins array at

three different cases: vertical based on horizontal fins ,vertical based on vertical fins and

horizontal based on vertical base . This work for a temperature range from 40 to 80 oC at three

different heights, namely 32mm, 60 mm and 90 mm. There result showed no affect of fin height

to the change of position, but the fin space is most effective for vertical fins based on vertical

base. The effects of changing. fin length from 250 to 375 mm on the rate of heal transfer and the

optimum fin spacing of vertical rectangular fins protruding from a horizontal or a vertical

rectangular base have been investigated by Leung. Probers and Shilston [4] experimentally

except fin length, other geometric parameters of several fin configurations were kept fixed for

considered orientations. There result concerned at a constant base temperature,40°C above

that of the ambient environment. The experimental measurements for vertical base showed that

the increase in fin length caused reduction in the rate of heat dissipation per unit base area from

the fin array. In addition, the optimal fin spacing rose from 10 ± 1mm to 11 ± 1 mm as a result of

fin length increase. On the other hand, with horizontal base, large reduction in the rate of heat

transfer per unit area occurred when the fin length was increased. The optimal fin. spacing of

horizontally based fin array increased from 11 ± 1 mm to 1 4 ± 1 mm as the fin length was

increased from 250 mm to 375 mm. All these consequences revealed that the effect of fin

length on heal transfer performance of fin arrays is significant.Walunj,.Daund,and .Palande




4

[5] studies various experimental have been made to investigate effect of fin height, fin spacing,

fin length and fin thickness over convective heat transfer. Effects of thermodynamic properties

like heat input, base-to-ambient temperature difference are also studied by many researchers.

Some investigators make known sets of correlations screening the relation between various

parameters of heat sink. Experiments are taken by some researchers for upward and downward

facing rectangular fins. Also, trivial investigation has been carried out for different angle of

inclination of the heat sink. The sensitivity of inclination over geometric parameters found to be

great importance

Welling and Wooldridge [ 6] performed another experimental study to compare actual

rectangular fin experiments with those of vertical plate, enclosed duct and parallel plate data from

previous studies. During the tests, guard heater plate was utilized to minimize the heat losses

from the sides and rear of the set-up. Data obtained from experiments showed that with closely

spaced fins, the heat transfer coefficients were smaller compared to wider fin spacing's, because

of boundary layer interference, which prevents air inflow. It was observed that the heat transfer

coefficients of finned arrays were smaller than those of vertical plate and greater than either those

of enclosed ducts or those of parallel plates. For a given base-to-ambient temperature difference,

an optimum H/s (fin height to fin spacing) ratio at which heat transfer coefficient is maximum

was determined from the considered fin configurations. Mi sandar Mon, Ulrich Gross [7]

reported that the effect of fin spacing on four row annular finned tube bundles in staggered and

inline arrangements are investigated by 3D numerical study. To investigate the velocity and

temperature distribution between fins. The flow behavior of the developing boundary layer, the

horse shoe vortex system, and thermal boundary layer developments in the annular finned tube

banks will be visualized.

Azimifar A., Payan S [8] study the optimization of characteristics of an array of thin fins using

PSO algorithm in confined cavities heated from a side with natural convection. Hossein Z. and

et.al. [9],investigate natural convection of a Nano fluid in an enclosure with an inclined local

thermal non-equilibrium porous fin considering with respect of fin spaces. However Emel Evren

S. and et.al . [10] experimentally study the effect of fins space on the transition to oscillating

laminar natural convection in an enclosure. Khalil K., Abdalla AlAmiri [11]reported that the

effect of fin space at laminar natural convection heat transfer in a differentially heated cavity

with a thin porous fin attached to the hot wall. Ilker T., Mehdi M [12] studies various

experimental have been made to investigate effect of fin height, fin spacing and fin length for

inclined position over convective heat transfer. Recently Rishikesh and Kiran [13] presented the

characterization of radial curved fin heat sink with the effect of fin heights.

II. Experimental methods:

The experimental apparatus is comprised of a rectangular fin as cross-section to the U-heater

shape direction in an open loop. The former is used to control the base temperature from 50 to

150 oC, and the latter sets the fins surface temperature. Figure 1. shows a schematic

representation of the test rig, which is divided into the lower part, where the tests are carried out

by different space and the upper part, where the power supply and temperatures gauges are work

together. The rectangular aluminum table has a dimensions (90 cm x 60 cm) prove the base of the


https://arc.aiaa.org/author/Azimifar%2C+A

https://arc.aiaa.org/author/Payan%2C+S

https://arc.aiaa.org/author/Zargartalebi%2C+Hossein

https://arc.aiaa.org/author/Selamet%2C+Emel+Evren


https://arc.aiaa.org/author/Khanafer%2C+Khalil

https://arc.aiaa.org/author/Alamiri%2C+Abdalla



5

fins on the heater. So that the base of the fins has a constant area for five sets of fins and this base

seek directly on the heater so that the transmitted heat conduction from the heater to the base of

fins that contains a row of fins is working to expel heat to the surrounding environment, with an

insulator between the heater and the base of the apparatus and demonstrate electrical panel

containing gauges and switches in the front of the base of the apparatus as observed in figures 1 .

Figure ( 1) Overall view of the experimental rig and associated instrument.

Five aluminum plates size (250 mm) * (250 mm) ,has thermal conductivity (233w/m²k) installed .

On each one set of aluminum fins each fin height and width are constant (50 mm &250 mm) has

the same surface area, number and the same specifications as the plates. The five sets of plate

contains (6 fins) separated by a distance (22 mm), and the second plat separated by a distance (27

mm), the third base has distance 30mm, fourth plate has space equal to 35mm, while the fifth

plat separated by a distance (38 mm) . Under each one fixed heater to gives temperature and

thermocouple to measure temperature.

Figure ( 2 ) Base of Aluminum plate with rectangular fins.

The three horizontal electrical U-heaters are placed on 70 mm above the experimental table to

avoid ground effect. Electrical heating coil with 2.25 kW capacity is kept inside the tube.

Thermal conductivity of aluminum is 236 W/mK.Heat transfer coefficients is important fin

parameters measured from the following formula: The heat transfer coefficient (h, w\m2 .K)) can

be estimated from the following equation: [14,15]

Q fin

h = --------------------- ------ (1)

At * ( Ts - T∞ )

Where: Q fin is the heat transfer from the fin surface at Ts ,

At is the total fin surface area,

T∞ is the ambient temperatures.




6

The fin efficiency of a any fin ,ηfin, is defined as:

=

) .............(2)

This relation enables us to determine the heat transfer from a fin when its efficiency is known.

But the overall fins efficiency is express by the following formula:

............................(3).

The performance of the fins judged on the basis of the enhancement in heat transfer relative to the

no-fin case . The performance of fins expressed in term of the fin effectiveness ϵf is defined as :

...................(4)

Fin thermal Resistance (Rfin) is defined as temperature rise per unit of power, analogous to

electrical resistance, and is expressed in units of degrees Celsius per watt (°C/W). If the device

dissipation in watts is known, and the total thermal resistance is calculated, the temperature rise

of the die over ambient can be calculated as express in the following formula: [14,15]

Rfin =

.........................(5)

This equation may be used to expression for the thermal resistance of a fin array. A small value

of thermal resistance indicates a small temperature drop across the heat sink, and thus a high fin

efficiency. Ro is an effective resistance that account of heat parallel flow paths for conduction-

convection in the fins and by convection from the prime surface. Equation 10 represent the

overall effective resistance Ro . The governing equation for one dimensional conduction with

convection is applicable to systems in which the lateral conduction resistance is small relative to

the convection resistance. Under these conditions the temperature profile is one dimensional. The

conditions for which Eq. (6) is valid are determined from the following criterion:

Bi=

<0.1 ...............................(6)

Where Bi is the Biot number based upon the maximum half thickness of the fin profile.

The fin Biot number is simply the ratio of the lateral conduction to lateral convection resistance: [

14 ]

Bi =

...............................(7)

III. Results and Discussions:

The mean point in our work is study the effect fin space to the fin thermal performance at very

important range base temperatures from 50 to 150 oC. This range of temperatures has a huge

application in the oil and gas industries and mechanical industries especially the heat exchanger

,internal combustion engine and power station . To examine the fin s heat performance for this

wide range of temperatures, we need to estimate a many parameters such as heat transfer

coefficient, fin effectiveness, fin efficiency, thermal resistance ,Biot number and heat transfer of




7

fin surface. It decide to fixed the five sets of array of rectangular fin at a cross direction to the

heater (power supply) as shown in the figure 3. There is an approximately linear relationship

between the heat transfer coefficient (h) for all base temperatures range used with fins space . As

the fin space increase the heat transfer coefficient decrease due to low distance between the

arrays of fins. The convection heat transfer rates from fin arrays and the vertical flat plate are

plotted as a function of base-to-ambient temperature difference for fin spacing, s1 = 22 mm(no.1),

s2 = 27 mm (no.2), s3 = 30 mm (no.3), s4 = 35 mm (no.4) and s5 = 38 mm (no.5)and for fin a

constant lengths, L = 250 mm , height [ H = 50 mm] and thickness [ 1mm] as illustrated in figure

1 and table 1 respectively. The results for examine the effect the fins space (s) is observed in

table.1 and figure.2 for morning time Am, but no big difference at the night Pm as found in the

measurements.

Table 1 The heat transfer coefficient for different space with the base temperature at Am.

Tb(K) h1( w ∕m²k) h2( w ∕m²k) h3( w ∕m²k) h4( w ∕m²k) h5( w ∕m²k)

323 189.8 160.33 136.36 113.12 91.46

343 105.4 88.91 76.52 60.65 49.5

363 82.86 69.95 59.75 47.14 37.13

383 57.91 47.01 39.57 33.51 28.85

403 46.6 38.05 32.05 27.04 23.77

423 37.4 30.81 25.6 23.01 20

Figure 3. The effect of fin space with heat transfer coefficient for different base temperature at Am

It is seen that the convective heat transfer coefficient from the fin arrays increases with decrease

the base temperature. The effect of extending the fin space from 22 mm to 38 mm results in

higher steady-state convective heat dissipation from the fin arrays. However, the curves

demonstrating the behaviors of fin spaced show decreasing the heat transfer coefficient with

increasing the fin space for all base temperature range. The heat transfer coefficient measured

from five fin spaced are close to each other at high base temperature whereas at low base

temperature, the heat transfer rates tend to diverge with the fine space. For increasing the heat

020406080

100120140160180200

323k 343k 363k 383k 403k 423k

He

at t

ran

sfe

r co

ffe

cie

nt

Base temperature (Tb)

h1( w ∕m²k) h2( w ∕m²k) h3( w ∕m²k) h4( w ∕m²k)




8

transfer rate we need the extends surface known a fin .Also, increasing the temperature difference

between the fins and environmental .The best equation to calculate the heat transfer rate for

rectangular fin is :[15]

Qfin = M * tanh (mL) ……………..(8)

Where: M=√ (Tb-T )

mL =√

*L

Figure 4. Fin heat transfer rate for five fin spaces at the base temperatures range.

It is very clear from the above figure increasing of fin heat transfer rate with decreasing the fin

space. This is because increasing the different between the surface fin temperatures with base

temperatures and increasing the heat transfer coefficient as shown in the previous figure .Fin

performance can be described in three different ways. The first is fin effectiveness (equation

no.4). It is the ratio of the fin heat transfer rate to the heat transfer rate of the object if it had no

fin and the ratio of the fin heat transfer rate to the heat transfer rate of the fin if the entire fin were

at the base temperature as defined as fin efficiency. Fin efficiency will always be less than one.

This is because assuming the temperature throughout the fin is at the base temperature would

increase the heat transfer rate. The third way fin performance can be described is with overall

surface efficiency as described in equation no.3. We used equations 3 to 8 for our calculation to

examine the fin thermal performance. Figure 5 represent the results of fin effectiveness with

different fine space to the a wide range of base temperature.

0

20

40

60

80

100

120

323k 343k 363k 383k 403k 423k

Fin

he

at t

ran

sfe

r


Qᶠ1 (W)

Qᶠ2 (W)

Qᶠ3 (W)

Qᶠ4(W)

Qᶠ5 (W)




9

Figure 5 Fin space with Effectiveness' at different base temperature in the morning condition

It is clear from this figure, fin effectiveness is increase with increasing the base temperatures and

fin space for rectangular shape. The results of fin effectiveness at the high temperatures more

than 100oC are very closed for five fin spaces. The second way for measure the performance is

calculate the efficiency for different space of fin at the range of temperatures used as shown in

figure 6 and table 2 at morning condition.

Table2. The results of efficiency for different fin space

Tb(K) Ƞᶠ1 Ƞᶠ2 Ƞᶠ3 Ƞᶠ4 Ƞᶠ5

323 0.4376 0.468 0.5048 0.544 0.5894

343 0.5593 0.589 0.6273 0.665 0.7142

363 0.6103 0.641 0.6777 0.719 0.7658

383 0.6839 0.716 0.7551 0.778 0.8081

403 0.7261 0.755 0.7898 0.808 0.8333

423 0.7645 0.791 0.8231 0.838 0.8588

Figure 6. Efficiency of fin with different space and base temperatures.

It is obvious from the above figure, the fin efficiency increase with the increasing the base

temperatures and the spaced fin. . In morning heat transfer coefficient is lesser than in the

0

0.2

0.4

0.6

0.8

1

323k 343k 363k 383k 403k 423k

Fin

eff

icie

ncy

Base remperature (Tb)

Ƞᶠ1 Ƞᶠ2 Ƞᶠ3 Ƞᶠ4 Ƞᶠ5

0

0.1

0.2

0.3

0.4

323k 343k 363k 383k 403k 423k

Fin

Eff

ect

ive

ne

ss


E 1

E 2

E 3

E 4

E 5




11

evening and efficiency will change according to this parameter. Efficiency of different space at

the night condition is 2.7% higher than the day condition. It shows that the efficiency of the fins

is changed according to the environmental condition. Figure 7. represent the overall efficiency for

five space between the two fins. The relationship is the same second way of measured the

performance for all spaces to the range of base temperatures from 50 to 150 oC.

Figure 7. The overall efficiency for different fin space at Am condition.

The results for three types of ways to examine the fin performance to the heat transfer is very

confirm, that’s increasing of fin performance with increasing the fin space. Also, the fin

performance increase with increasing the base temperatures. Thermal resistance is defined as

temperature rise per unit of power, analogous to electrical resistance, and is expressed in units of

degrees Celsius per watt (°C/W). If the device dissipation in watts is known, and the total thermal

resistance is calculated, the temperature rise of the die over ambient can be calculated as express

in formula no. 10.Tthe most important think is the calculation of overall thermal resistance

Rto:[15]

Rt.o =

………(10)

The results for effects the fin space with thermal resistance is illustrate in figure 8 .

Figure 8. Fin thermal resistance against the base temperate for five fin space.

It is clear from this figure there is a linear relation between the base temperatures with fin thermal

resistance for different fin spaces. Also, there is increasing of fin thermal resistance with

increasing the fin space due to the decreasing the heat transfer coefficients of fins. The same

0

0.2

0.4

0.6

0.8

1

1.2

323k 343k 363k 383k 403k 423k

Fin

th

erm

al r

esi

stan

ce


Rt.ƒ1(Ω)

Rt.ƒ2(Ω)

Rt.ƒ3(Ω)

Rt.ƒ4(Ω)

Rt.ƒ5(Ω)

0

0.2

0.4

0.6

0.8

1

323k 343k 363k 383k 403k 423k

Fin

ove

rall

eff

icie

ncy


Ƞ˳1

Ƞ˳2

Ƞ˳3

Ƞ˳4

Ƞ˳5




11

relationship it's found for overall thermal resistance with different five fin space as shown in

figure 9 and table 3 with very closed results for all the range of base temperatures used from 50 to

150 oC.

Figure 9. Overall thermal resistance at five fin space with base temperatures.

Table 3 Overall thermal resistance according to different base temp. for five fin space.

Tb(K) Rt.ₒ1(Ω) Rt.ₒ2(Ω) Rt.ₒ3(Ω) Rt.ₒ4(Ω) Rt.ₒ5(Ω)

323 0.0219 0.0235 0.0241 0.0268 0.0283

343 0.0321 0.0338 0.0351 0.0383 0.0411

363 0.0428 0.0456 0.0482 0.0503 0.0521

383 0.0561 0.0579 0.0596 0.0616 0.0633

403 0.0663 0.0688 0.0711 0.0717 0.0752

423 0.0792 0.0821 0.0854 0.0861 0.0871

Biot no. is the ratio determines whether or not the temperatures inside a body will vary

significantly in space, while the body heats or cools over time, from a thermal gradient applied to

its surface. In general, problems involving small Biot numbers (much smaller than 1) are

thermally simple, due to uniform temperature fields inside the body. Biot numbers much larger

than 1 signal more difficult problems due to non-uniformity of temperature fields within the

object. The Biot number has a variety of applications, including transient heat transfer and use in

extended surface heat transfer calculations. In this work the Biot number is examined for

different fin space to the big range of base temperatures from 50 to 150 oC as illustrated in figure

10 and table 4 for morning condition.

0

0.02

0.04

0.06

0.08

0.1

323k 343k 363k 383k 403k 423k

The

rmal

re

sist

ance

fo

r fi

n a

rray


Rt.ₒ1(Ω)

Rt.ₒ2(Ω)

Rt.ₒ3(Ω)

Rt.ₒ4(Ω)

Rt.ₒ5(Ω)




12

Figure 10. Biot no. at different base temperatures for many fin space at Am

.

It is clear from the above figure, that’s Biot no. very small and less than 1 for all space of fin

used. This mean uniform distributions of surface fin for rectangular shape. Also, it's found there

is an inverse relation between the base temperatures and Biot no. for all space used. There is a

closed results of Biot no. at high temperature up than 100oC .

Conclusion:

The following conclusion can deduced from the present work:

1) It is found the heat transfer coefficient depends upon the space, temperatures and types of

material. If there are changes in environmental conditions, there is a small changes in heat

transfer co-efficient and efficiency also.

2) Average heat transfer increase with decreasing the fin space in natural convection mode.

3) The range of Biot no. for all fin spaces is from 0.004 to 0.043,this mean a good distribution in

the surface of rectangular fin .

4) The range of effectiveness for different fin spaces is from 0.27 to 0.33 less than one.

5) As the fin spaces increase the overall thermal resistance, overall fin efficiency and fin

effectiveness increase also.

6) No optimum fin space found in this research at the range from 22 to 38 mm.

References:

[1] Starner K.E. and McManus H.N., “An Experimental Investigation of Free Convection Heat

Transfer from Rectangular Fin Arrays”, Journal of Heat Transfer, 273-278, (1963) .

[2] Leung C.W. and Probert S.D., “Thermal Effectiveness of Short-Protrusion Rectangular, Heat-

Exchanger Fins”, Applied Energy, 1-8, (1989) .

0

0.01

0.02

0.03

0.04

0.05

323k 343k 363k 383k 403k 423k

Bio

t N

O.


Bᵢ1 Bᵢ2 Bᵢ3 Bᵢ4 Bᵢ5




13

[3] Leung C.W., Probert S.D. and Shilston H.A., “Heat Exchanger Design: Thermal Performances of

Rectangular Fins Protruding from vertical or Horizontal Rectangular Bases”, Applied Energy, 123-

140, (1985).

[4] Leung C.W., Probert S.D. and Shilston H.A., “Heat Transfer Performances of Vertical Rectangular

Fins Protruding from Rectangular Bases: Effect of Fin Length”, Applied Energy, 313-318, (1986).

[5] Walunj,A.A., Dound V.S. and Poland, D.D. ,Heat transfer performance of free convection,

International Journal of Innovation and Applied Studies ISSN 2028-9324 Vol.6No.2June2014, pp.232-

238., 2014

[6] Welling J.R. and Wooldridge C.N., “Free Convection Heat Transfer Coefficients from Vertical

Fins”, Journal of Heat Transfer, 439-444, (1965).

[7] Mi sandar Mon, Ulrich Gross “Numerical study of fin spacing effects in annular finned tube heat

exchanger”, International Journal of Heat and Mass Transfer 47, 1953–1964.,2004.

[8]Azimifar A., Payan S.’ Optimization of characteristics of an array of thin fins using PSO algorithm

in confined cavities heated from a side with free convection. Applied Thermal Engineering 110, 1371-

1388, 2017.

[9]Hossein Z., Mohammad G., Aminreza N., Ali. J. “ Natural convection of a Nano fluid in an

enclosure with an inclined local thermal non-equilibrium porous fin considering Buongiorno’s model.

Numerical Heat Transfer, Part A: Applications 70:4, 432-445, 2016

[10] Emel Evren S, Ahmet S., Deaconescu T., Deaconescu.A. , Effect of Fins on the Transition to

Oscillating Laminar Natural Convection in an Enclosure. MATEC Web of Conferences 70, 07002, 2016.

[11] Khalil K., Abdalla AlAmiri, Joe Bull. , Laminar natural convection heat transfer in a differentially

heated cavity with a thin porous fin attached to the hot wall. International Journal of Heat and Mass

Transfer, Vol. 87, 59-70, 2015

[12] Ilker T., Mehdi M.,Natural convection heat transfer from inclined plate fin heat sinks,

International journal of heat and mass transfer,56,574-593, 2013

[13] Rishikesh K. and Kiran B. , Characterization of radial curved fin heat sink

Under Natural and Forced Convection, IOP Conf. Series Materials Science and Eng. 310 ,012030tube

heat exchanger” , International Journal of Heat and Mass Transfer 47 (2004) 1953–1964, 2018.

[14] Incropera F.P., De witt D.P. "Fundamentals of heat and mass transfer. 4th Edition. john Wiley &

Sons, No 147- 172., 2003.

[15] Cengel Yunus A., Heat transfer: A Practical Approach,2nd

edition SI McGraw Hill Higher

Education-ISBN 0-07-245893-3, 1996.


https://arc.aiaa.org/author/Azimifar%2C+A

https://arc.aiaa.org/author/Payan%2C+S

https://arc.aiaa.org/author/Zargartalebi%2C+Hossein

https://arc.aiaa.org/author/Ghalambaz%2C+Mohammad

https://arc.aiaa.org/author/Noghrehabadi%2C+Aminreza

https://arc.aiaa.org/author/Chamkha%2C+Ali+J


https://arc.aiaa.org/author/Selamet%2C+Ahmet

https://arc.aiaa.org/author/Deaconescu%2C+T

https://arc.aiaa.org/author/Deaconescu%2C+A

https://arc.aiaa.org/author/Khanafer%2C+Khalil

https://arc.aiaa.org/author/Alamiri%2C+Abdalla

https://arc.aiaa.org/author/Bull%2C+Joe

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